Free-form optimization method for frame structures aiming at controlling time-dependent responses

• Published in: Structural and multidisciplinary optimization Vol. 63; no. 1; pp. 479 - 497
• Main Authors: Shimoda, Masatoshi, Liu, Yang, Wakasa, Mamoru
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 2021; Springer Nature B.V
• Subjects: Computational Mathematics and Numerical Analysis; Control methods; Design optimization; Engineering; Engineering Design; Forced vibration; Frame structures; Free form; Free vibration; Function space; Industrial Application Paper; Lagrange multiplier; Optimization; Parameter sensitivity; Sensitivity; Smoothness; Theoretical and Applied Mechanics; Time dependence; Transient response; Free-form; Transient response; Time-dependent; Frame structures; Forced vibration; Parameter-free
• ISSN: 1615-147X; 1615-1488
• DOI: 10.1007/s00158-020-02708-y

In this paper, a parameter-free optimization method for controlling the time-dependent response of frame structures is proposed. The proposing method deals with three optimization problems, including a vibration displacement minimization problem, a vibration displacement control problem, and a dynamic compliance minimization problem, which is the special case of the vibration minimization problems. These time-dependent optimum design problems are formulated as distributed-parameter optimization problems and the sensitivity functions for the shape variation to obtain the optimal shape are derived based on the material derivative method, Lagrange multiplier method, and the adjoint method. The derived sensitivity function is applied to the H 1 gradient method for frames, which is a gradient method in the function space to determine the optimal shape variation. With the proposed method, the optimal shape for time-dependent response problems such as a forced vibration, a free vibration, or a transient response is obtained while minimizing the objective functional and maintaining the smoothness of a frame structure. Several numerical design examples including a continuous dynamic force or an impulse force as an input force are shown to verify and validate the effectiveness of the proposed method and the results are discussed.